{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T09:00:13Z","timestamp":1768899613559,"version":"3.49.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":23638,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1949,6,23]]},"abstract":"<jats:p>In a paper J. \u0141ukasiewicz and A. Tarski study the systems arising out of the implication function <jats:italic>C (x, y)<\/jats:italic> = min(1, 1 \u2013 <jats:italic>x<\/jats:italic> + <jats:italic>y<\/jats:italic>) and the negation function <jats:italic>Nx<\/jats:italic> = 1 \u2013 <jats:italic>x<\/jats:italic>, where <jats:italic>x, y<\/jats:italic> are real numbers between 0 and 1 inclusive. Let us then write\n<jats:italic>\u0421xy<\/jats:italic> = <jats:italic>min(1, 1 \u2013 x + y) and Nx = 1 \u2013 x<\/jats:italic>. (1)<\/jats:p><jats:p>In this note we shall consider another implication function, namely\n<jats:italic>\u0421\u2032<jats:sub>xy<\/jats:sub> = \u0421\u0421N<jats:sub>xyy<\/jats:sub><\/jats:italic>, (2)<\/jats:p>","DOI":"10.2307\/2266509","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T15:05:25Z","timestamp":1146927925000},"page":"95-97","source":"Crossref","is-referenced-by-count":34,"title":["On an implication function in many-valued systems of logic"],"prefix":"10.1017","volume":"14","author":[{"given":"Z. P.","family":"Dienes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200072649","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,8]],"date-time":"2019-06-08T06:31:27Z","timestamp":1559975487000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200072649\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1949,6,23]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1949,6,23]]}},"alternative-id":["S0022481200072649"],"URL":"https:\/\/doi.org\/10.2307\/2266509","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1949,6,23]]}}}